数学的实践与认识
數學的實踐與認識
수학적실천여인식
MATHEMATICS IN PRACTICE AND THEORY
2009年
18期
144-148
,共5页
上协边类%(Z_2)~k作用%不动点集%射影丛
上協邊類%(Z_2)~k作用%不動點集%射影叢
상협변류%(Z_2)~k작용%불동점집%사영총
cobordism class%(Z_2)~k-action%fixed point set%projective bundle
设(Z_2)~k作用于光滑闭流形Mn上,其不动点集具有常维数n-r,J~r_(n,k)是具有上述性质的未定向的n维上协边类[M~n]构成的集合.通过构造上协边环MO*的一组生成元决定了J~((2~k)+(2~(k-1))-2)_(*,k)的结构.
設(Z_2)~k作用于光滑閉流形Mn上,其不動點集具有常維數n-r,J~r_(n,k)是具有上述性質的未定嚮的n維上協邊類[M~n]構成的集閤.通過構造上協邊環MO*的一組生成元決定瞭J~((2~k)+(2~(k-1))-2)_(*,k)的結構.
설(Z_2)~k작용우광활폐류형Mn상,기불동점집구유상유수n-r,J~r_(n,k)시구유상술성질적미정향적n유상협변류[M~n]구성적집합.통과구조상협변배MO*적일조생성원결정료J~((2~k)+(2~(k-1))-2)_(*,k)적결구.
Let J~r_(n,k) denote the set of n-dimensional cobordism classes containing a representative M~n admitting a (Z_2)~k-action with fixed point set of constant codimension r. In this paper special generators of the unoriented cobordism ring MO, are constructed to determine the groups J~((2~k)+(2~(k-1))-2)_(*,k).
